Use the functions $f (x) = x^{2} - 3 x - 18$ and $g (x) = x^{2} + 3 x - 18$ to answer parts (a) through $(g)$ .
(a) Solve $f (x) = 0$ .
(d) Solve $f (x) > 0$ .
(g) Solve $f (x) \geq 1$ .
(b) Solve $g (x) = 0$ .
(e) Solve $g (x) \leq 0$ .
(c) Solve $f (x) = g (x)$ .
(f) Solve $f (x) > g (x)$ .
(a) The solution set is ${- 3, 6}$ .
(Use a comma to separate answers as needed.)
(b) The solution set is
(Use a comma to separate answers as needed.)
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Final Answer: The solution set is $- 3, 6$ .

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Step 1 ：The first question asks to solve the equation $f (x) = 0$ . This is a quadratic equation and can be solved using the quadratic formula $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , where $a$ , $b$ , and $c$ are the coefficients of the quadratic equation $a x^{2} + b x + c = 0$ . In this case, $a = 1$ , $b = - 3$ , and $c = - 18$ .

Step 2 ：The solutions to the equation $f (x) = 0$ are $x = - 3$ and $x = 6$ . These are the x-values where the function $f (x)$ intersects the x-axis.

Step 3 ：Final Answer: The solution set is $- 3, 6$ .

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